Accelerating Optimal Power Flow with GPUs: SIMD Abstraction of Nonlinear Programs and Condensed-Space Interior-Point Methods

This paper introduces a novel computational framework for solving alternating current optimal power flow (ACOPF) problems using graphics processing units (GPUs). While GPUs have demonstrated remarkable performance in various computing domains, their application in AC OPF has been limited due to challenges associated with porting sparse automatic differentiation (AD) and sparse linear solver routines to GPUs. We aim to address these issues with two key strategies. First, we utilize a single-instruction, multiple-data (SIMD) abstraction of nonlinear programs (NLP). This approach enables the specification of model equations while preserving their parallelizable structure, and in turn, facilitates the implementation of AD routines that can exploit such structure. Second, we employ a condensed-space interior-point method (IPM) with an inequality relaxation strategy. This technique involves relaxing equality constraints to inequalities and condensing the Karush-Kuhn-Tucker system into a much smaller positive definite system. This strategy offers the key advantage of being able to factorize the KKT matrix without numerical pivoting, which in the past has hampered the parallelization of the IPM algorithm. By combining these two strategies, we can perform the majority of operations on GPUs while keeping the data residing in the device memory only. Comprehensive numerical benchmark results showcase the substantial computational advantage of our approach. Remarkably, for solving large-scale AC OPF problems to a moderate accuracy, our implementations -- MadNLP.jl and ExaModels.jl -- running on NVIDIA GPUs achieve an order of magnitude speedup compared to state-of-the-art tools running on contemporary CPUs.